Striped Sphere - hide backfaces
As far as I know you will probably have to use Node materials for this, I don't think there is any backface-culling options in Blender Internal Render by default, only through node materials.

Active node materials for your Blue Material, add the Blue Material to the default Material node from the dropdown menu.

Now add a new Input > Geometry node and use the Front/Back socket to control the transparency of the material by connecting it to the Alpha socket of the Output node